How to build a planar Brownian motion from a simple path and loops

par Isao Sauzedde (ENS Lyon)

mardi 18 nov. 2025, 09:50 → 10:50 Europe/Paris

Amphi Schwartz

The SLE2 path is the limit in the continuum of the 2D loop-erased random walk. The Brownian loop soup is a Poisson random set of loops in the plane. In 2003, Lawler and Werner conjectured that, by attaching to the former random simple path (i.e. without self-intersection) the loops  from the latter set, one should obtained a parameterised path which is a Brownian motion. I will present results we obtained with Nathanaël Berestycki which allow us to prove this conjecture. Most of the talk will be dedicated to the presentation of the "attachment" procedure and of its continuity properties. If there is enough time left, I will shortly present continuum objects we may be able to construct with this procedure, such as scaling limits of unicycle forests. No prerequisite knowledge is assumed. The talk will be in english.